Acid gas is removed from a high pressure feed gas that contains significant quantities of CO2 and H2S. In especially preferred configurations and methods, feed gas is contacted in an absorber with a lean and an ultra-lean solvent that are formed by flashing rich solvent and stripping a portion of the lean solvent, respectively. Most preferably, the flash vapors and the stripping overhead vapors are recycled to the feed gas/absorber, and the treated feed gas has a CO2 concentration of less than 2 mol % and a H2S concentration of less than 10 ppmv, and more typically less than 4 ppm.